Yousef is given a tree$$$^{\text{∗}}$$$ of $$$n$$$ vertices numbered from $$$1$$$ to $$$n$$$.

Let $$$S$$$ be the set of all leaves$$$^{\text{†}}$$$ of the given tree (this set is determined from the original tree and does not change).

Yousef repeats the following process until the number of unchosen vertices is at most one:

Choose two distinct vertices $$$u, v \in S$$$ that have not been chosen before.
Add $$$d(u, v)$$$ to the total cost, where $$$d(u, v)$$$ is the number of edges on the simple path between $$$u$$$ and $$$v$$$.
Mark $$$u$$$ and $$$v$$$ as chosen.

Your task is to help Yousef determine the minimum possible total cost achievable after the process ends.

$$$^{\text{∗}}$$$A tree is an undirected connected graph in which there are no cycles.

$$$^{\text{†}}$$$A leaf of a tree is a vertex that is connected to at most one other vertex.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow.

Each test case consists of several lines. The first line of the test case contains an integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5$$$) — the number of vertices in the tree.

Then $$$n − 1$$$ lines follow, each of which contains two integers $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \ne v$$$) that describe a pair of vertices connected by an edge. It is guaranteed that the given graph is a tree and has no loops or multiple edges.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the minimum possible total cost achievable after the process ends.

Note

In the first test case, the set of leaves $$$S$$$ contains $$$\{1, 3, 4\}$$$. Yousef can do the following:

Choose $$$u = 1$$$, $$$v = 3$$$, with $$$d(1, 3) = 2$$$. Yousef adds $$$2$$$ to the total cost and marks vertices $$$1$$$ and $$$3$$$ as chosen.

Since there is one vertex left unchosen, the process stops, and the total cost is $$$2$$$. It can be shown that $$$2$$$ is the minimum answer.

$\text{[math]}$ The given tree in the first test case.

In the second test case, the set of leaves $$$S$$$ contains $$$\{1, 3, 5, 6\}$$$. Yousef can do the following:

Choose $$$u = 1$$$, $$$v = 3$$$, with $$$d(1, 3) = 2$$$. Yousef adds $$$2$$$ to the total cost and marks vertices $$$1$$$ and $$$3$$$ as chosen.
Choose $$$u = 5$$$, $$$v = 6$$$, with $$$d(5, 6) = 2$$$. Yousef adds $$$2$$$ to the total cost and marks vertices $$$5$$$ and $$$6$$$ as chosen.

Since there is no vertex left unchosen, the process stops, and the total cost is $$$4$$$.

$\text{[math]}$ The given tree in the second test case.

Fallen Leaves

Examples